(1) BP1934 reports that "This family is descended from Engeler, who held of the King, according to Domesday Book, two hides of land in the manor of Chichester, Sussex, from which his descendants derived their surname."
(2) Vivian shows 2 alternative ancestries for the Sir John who married Thomasin de Ralegh, one being "from Harl. MS. 1538, fo.256, and the College of Arms" and the other being from a "History of the family" as provided by one of its descendants (Sir Alexander Palmer Bruce Chichester, Bart, who lived 1842-1881). We show both versions but, as the second one is just slightly supported by BP1934 (which starts by showing that Sir John as son of Sir Roger which is at least consistent with the second version, we show the first in italics.
(3) Vivian reports that the 'College of Arms' pedigree starts with the following Walleran who was "descended from a brother of Robert Chichester, Bishop of Exeter, temp. King Stephen" (who r. 1135-1154).